average-precision

In this question I asked clarifications about the precision-recall curve. In particular, I asked if we have to consider a fixed number of rankings to draw the curve or we can reasonably choose ourselves. According to the answer , the second one is correct. However now I have a big doubt about the Average Precision (AP) value: AP is used to estimate numerically how good is our algorithm given a certain query. Mean Average Precision (MAP) is average precision on multiple queries. My doubt is: if AP changes according to how many objects we retrieve then we can tune this parameter to our advantage